An urn has $5$ white and $10$ black balls. A die is rolled, and that many balls is drawn from the >urn. What is the probability that all the balls drawn are white?

My thinking is that each die roll $(d)$ has probability $\frac{1}{6}$. The probability to get only white balls from your draw is $$\frac{C(5, d)}{C(15, d)}$$. Then you add up all the probabilities. I come up with $\frac{5}{66}$, but have no way of knowing if I'm right. Is this the way to go about it? I tried multiplying the probabilities tied to each die roll and came up with an extremely small chance, so that seems wrong to me.

Your idea looks right to me. As the die roll gets large, the chance of all white balls gets very small. For the first two, we have $\frac 16\cdot \frac 5{15}+\frac 16\cdot \frac5{15}\cdot \frac 4{14}=\frac 1{18}\cdot \frac {18}{14}=\frac 1{14}=\frac 5{70}$, which is not much less than $\frac 5{66}$